Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.2s (24.1%)

Symmetry

(sort alpha beta)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

689×	`distribute-rgt-in_binary64`
661×	`distribute-lft-in_binary64`
470×	`associate-l_binary64`
388×	`associate-+r+_binary64`
387×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	38
2	117	38
3	625	37
4	4291	37
5	4944	37

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.9b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
▶	2.4b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))

Status

Error

Program

2.9b

(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

▶

2.4b

(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))

Compiler

Compiled 190 to 127 computations (33.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3)))
✓	0.0b	(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))
✓	0.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))
✓	18.9b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2))))

series127.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

75.0ms	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))
30.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2))))
14.0ms	(/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3)))
7.0ms	(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))

rewrite45.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

201×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
193×	`add-cbrt-cube_binary64`
189×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	70
1	398	70

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

42.0ms	(/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3)))
42.0ms	(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))
42.0ms	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))
42.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2))))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
798×	`times-frac_binary64`
289×	`+-commutative_binary64`
228×	`associate-+r+_binary64`
181×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	762	8369
1	2739	8280

Stop Event

1×	node limit

Counts

217 → 229

prune439.0ms (8.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	223	6	229
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	6	231

Error

0.0b

Counts

231 → 6

Alt Table

Status	Error	Program
	1.7b	(/.f64 (.f64 (+.f64 1 alpha) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2))) (+.f64 beta (+.f64 alpha 3)))
	0.2b	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))
	2.4b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (fma.f64 beta 4 (+.f64 (fma.f64 alpha alpha 4) (fma.f64 beta beta (fma.f64 alpha 4 (.f64 (*.f64 2 beta) alpha)))))))
▶	0.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))
	8.8b	(/.f64 (.f64 (+.f64 beta 1) (+.f64 1 alpha)) (.f64 (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2) (+.f64 beta (+.f64 alpha 3))))
	2.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2))) 2) (cbrt.f64 (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2)))))

Compiler

Compiled 13865 to 10171 computations (26.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 alpha (+.f64 beta 2)))
	0.0b	(/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3)))
✓	0.0b	(*.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))))
✓	0.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))

series141.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

97.0ms

(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (*.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))

33.0ms

(*.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))))

10.0ms

(/.f64 1 (+.f64 alpha (+.f64 beta 2)))

rewrite44.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`
194×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	417	57

Stop Event

1×	node limit

Counts

3 → 95

Calls

3 calls:

42.0ms

(/.f64 1 (+.f64 alpha (+.f64 beta 2)))

42.0ms

(*.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))))

42.0ms

(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (*.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
755×	`times-frac_binary64`
258×	`+-commutative_binary64`
202×	`associate-+r+_binary64`
175×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	705	7516
1	2575	7491

Stop Event

1×	node limit

Counts

167 → 178

prune433.0ms (8.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	233	6	239

Error

0.0b

Counts

239 → 6

Alt Table

Status	Error	Program
	2.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2))) 2) (cbrt.f64 (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2)))))
	6.1b	(/.f64 (+.f64 1 beta) (*.f64 (/.f64 (+.f64 beta (+.f64 alpha 3)) (+.f64 alpha 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)))
	1.7b	(/.f64 (.f64 (+.f64 1 alpha) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2))) (+.f64 beta (+.f64 alpha 3)))
▶	0.2b	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))
	2.4b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (fma.f64 beta 4 (+.f64 (fma.f64 alpha alpha 4) (fma.f64 beta beta (fma.f64 alpha 4 (.f64 (*.f64 2 beta) alpha)))))))
✓	0.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))

Compiler

Compiled 14597 to 10746 computations (26.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3)))
✓	0.1b	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2)))
✓	0.3b	(pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2)

series164.0ms (3.2%)

Counts

3 → 56

Calls

3 calls:

84.0ms

(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))

49.0ms

(pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2)

30.0ms

(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2)))

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

201×	`add-sqr-sqrt_binary64`
198×	`log1p-expm1-u_binary64`
198×	`expm1-log1p-u_binary64`
193×	`add-cbrt-cube_binary64`
189×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	66
1	408	62

Stop Event

1×	node limit

Counts

3 → 73

Calls

3 calls:

37.0ms

(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))

37.0ms

(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2)))

37.0ms

(pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2)

simplify105.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
664×	`fma-def_binary64`
592×	`associate-/l*_binary64`
204×	`+-commutative_binary64`
164×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	615	6677
1	2275	6550

Stop Event

1×	node limit

Counts

129 → 149

prune455.0ms (8.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	205	5	210

Error

0.0b

Counts

210 → 5

Alt Table

Status	Error	Program
	1.7b	(/.f64 (.f64 (+.f64 1 alpha) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2))) (+.f64 beta (+.f64 alpha 3)))
▶	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3))))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))
	2.4b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (fma.f64 beta 4 (+.f64 (fma.f64 alpha alpha 4) (fma.f64 beta beta (fma.f64 alpha 4 (.f64 (*.f64 2 beta) alpha)))))))
✓	0.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))
	6.1b	(/.f64 (+.f64 1 beta) (*.f64 (/.f64 (+.f64 beta (+.f64 alpha 3)) (+.f64 alpha 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)))

Compiler

Compiled 12510 to 9305 computations (25.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3)))
✓	0.1b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3))))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))
	0.2b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2)))
	0.3b	(pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2)

series97.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

81.0ms

(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3))))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))

16.0ms

(/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3)))

rewrite29.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

207×	`add-sqr-sqrt_binary64`
206×	`expm1-log1p-u_binary64`
205×	`log1p-expm1-u_binary64`
198×	`add-cbrt-cube_binary64`
194×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	427	44

Stop Event

1×	node limit

Counts

2 → 41

Calls

2 calls:

28.0ms

(/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3)))

28.0ms

(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3))))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

731×	`times-frac_binary64`
652×	`associate-/r*_binary64`
561×	`associate-/l*_binary64`
522×	`fma-def_binary64`
194×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	555	5767
1	2022	5745

Stop Event

1×	node limit

Counts

89 → 101

prune353.0ms (6.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	201	5	206

Error

0.0b

Counts

206 → 5

Alt Table

Status	Error	Program
	1.7b	(/.f64 (.f64 (+.f64 1 alpha) (.f64 (+.f64 beta 1) (pow.f64 (+.f64 alpha (+.f64 beta 2)) -2))) (+.f64 beta (+.f64 alpha 3)))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 1 alpha) (+.f64 beta (+.f64 alpha 3))))) (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 alpha (+.f64 beta 2))) 2))
	2.4b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (fma.f64 beta 4 (+.f64 (fma.f64 alpha alpha 4) (fma.f64 beta beta (fma.f64 alpha 4 (.f64 (*.f64 2 beta) alpha)))))))
✓	0.1b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))))
	6.1b	(/.f64 (+.f64 1 beta) (*.f64 (/.f64 (+.f64 beta (+.f64 alpha 3)) (+.f64 alpha 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)))

Compiler

Compiled 12617 to 9485 computations (24.8% saved)

regimes758.0ms (14.9%)

Accuracy

Total 0.1b remaining (83.4%)

Threshold costs 0.1b (83.4%)

Counts

167 → 1

Compiler

Compiled 18896 to 14360 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	29	43

Stop Event

1×

saturated

end279.0ms (5.5%)

Compiler: Compiled 260 to 190 computations (26.9% saved)

Details

analyze4.0ms (0.1%)

sample1.2s (24.1%)

simplify26.0ms (0.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series127.0ms (2.5%)

rewrite45.0ms (0.9%)

simplify95.0ms (1.9%)

prune439.0ms (8.6%)

localize13.0ms (0.2%)

series141.0ms (2.8%)

rewrite44.0ms (0.9%)

simplify97.0ms (1.9%)

prune433.0ms (8.5%)

localize14.0ms (0.3%)

series164.0ms (3.2%)

rewrite39.0ms (0.8%)

simplify105.0ms (2.1%)

prune455.0ms (8.9%)

localize16.0ms (0.3%)

series97.0ms (1.9%)

rewrite29.0ms (0.6%)

simplify70.0ms (1.4%)

prune353.0ms (6.9%)

regimes758.0ms (14.9%)

simplify2.0ms (0%)

end279.0ms (5.5%)

Profiling